{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 12\n",
    "\n",
    "# 函数变换\n",
    "Book_3《数学要素》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "147dfa90-6f50-4bef-a6a2-412da8d16514",
   "metadata": {},
   "source": [
    "这段代码展示了函数 $$f(x) = 2e^{-(x - 1)^2}$$ 在各种几何变换下的曲线效果，包括平移、缩放以及对称变换。通过这些操作，展示了一个高斯函数的多种变换可能性。具体变换包括：\n",
    "\n",
    "1. **垂直平移**：将函数沿 y 轴方向平移，计算 $$f(x) + c$$ 来实现。在代码中取 $c=2$ 和 $c=-3$，以观察曲线在 y 轴上向上或向下移动。\n",
    "2. **水平平移**：将函数沿 x 轴方向平移，通过计算 $$f(x + c)$$ 实现。在代码中取 $c=3$ 和 $c=-1$，使得曲线在 x 轴上向右或向左移动。\n",
    "3. **垂直缩放**：改变函数的 y 方向幅度，通过计算 $$c \\cdot f(x)$$ 实现。在代码中，$c$ 取值为 $1/2$ 和 $2$，缩放曲线的 y 值，使其在 y 方向上变窄或变宽。\n",
    "4. **水平缩放**：通过调整自变量的系数改变函数在 x 轴上的伸缩性，计算 $$f(c \\cdot x)$$ 实现。在代码中，$c$ 取值为 $1/2$ 和 $2$，使得曲线在 x 方向上被压缩或拉伸。\n",
    "5. **关于 x 轴和 y 轴的对称**：对曲线进行对称变换。关于 x 轴的对称变换取 $$-f(x)$$，将曲线上下翻转。关于 y 轴的对称变换取 $$f(-x)$$，使曲线左右翻转。\n",
    "\n",
    "每种变换效果展示在单独的图形中，原始曲线用蓝色表示，变换后的曲线用红色表示。通过这些变换，可以直观展示函数的各种几何变化效果，包括位置、形状和方向上的调整，从而更好地理解函数的行为。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bdfd03b6-c180-4432-b548-dc1d648425a5",
   "metadata": {},
   "source": [
    "## 导入包"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b5d596be-6db1-4c8e-9187-28cfd6a1e573",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt  # 导入matplotlib库，用于绘图\n",
    "import numpy as np\n",
    "from sympy.abc import x\n",
    "from sympy import exp, lambdify"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff3ab51d-a2d5-47f6-a596-24061d56abd2",
   "metadata": {},
   "source": [
    "## 自定义函数plot_curve，绘制原始和变换后的曲线"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2f73b087-c095-4a7b-85d9-c9aff81d27d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_curve(x_array, y_array, \n",
    "               x_array_new, y_array_new):  # 绘制原始和变换后的曲线函数\n",
    "    fig, ax = plt.subplots()  # 创建图形对象和坐标轴对象\n",
    "    \n",
    "    plt.plot(x_array, y_array, color='#0070C0', label='Original')  # 绘制原始曲线\n",
    "    ax.fill_between(x_array, y_array, edgecolor='none', facecolor='#0070C0', alpha=0.2)  # 填充原始曲线下方区域\n",
    "    \n",
    "    plt.plot(x_array_new, y_array_new, color='r', label='Transformed')  # 绘制变换后的曲线\n",
    "\n",
    "    plt.xlabel('x')  # 设置x轴标签\n",
    "    plt.ylabel('y')  # 设置y轴标签\n",
    "    plt.axhline(y=0, color='k', linestyle='-')  # 添加水平轴\n",
    "    plt.axvline(x=0, color='k', linestyle='-')  # 添加垂直轴\n",
    "    plt.xticks(np.arange(-4, 5, step=1))  # 设置x轴刻度\n",
    "    plt.yticks(np.arange(-4, 5, step=1))  # 设置y轴刻度\n",
    "    plt.axis('scaled')  # 设置坐标比例\n",
    "    \n",
    "    ax.set_xlim(-4, 4)  # 设置x轴范围\n",
    "    ax.set_ylim(-4, 4)  # 设置y轴范围\n",
    "    ax.spines['top'].set_visible(False)  # 隐藏顶部边框\n",
    "    ax.spines['right'].set_visible(False)  # 隐藏右侧边框\n",
    "    ax.spines['bottom'].set_visible(False)  # 隐藏底部边框\n",
    "    ax.spines['left'].set_visible(False)  # 隐藏左侧边框\n",
    "    \n",
    "    plt.legend()  # 添加图例\n",
    "    ax.grid(linestyle='--', linewidth=0.25, color=[0.5, 0.5, 0.5])  # 添加网格\n",
    "    plt.rcParams[\"figure.figsize\"] = [7.50, 3.50]  # 设置图形大小\n",
    "    plt.rcParams[\"figure.autolayout\"] = True  # 自动布局"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d78f094f-23f6-4327-8caa-332219f37762",
   "metadata": {},
   "source": [
    "## 数据和函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "73e54f95-c478-4881-8ac4-506897138bd7",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_array = np.arange(-4, 4 + 0.01, step=0.01)  # 定义x轴范围\n",
    "\n",
    "f_x = 2 * exp(-(x - 1)**2)  # 定义原始函数f(x)\n",
    "f_x_fcn = lambdify([x], f_x)  # 将f(x)转换为可计算形式\n",
    "f_x_array = f_x_fcn(x_array)  # 计算原始函数的值"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "216ca088-ee23-4489-9acd-b6ca8e9a540f",
   "metadata": {},
   "source": [
    "## 垂直平移"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "17d1a68e-a9f1-4edb-84b0-cba7c727345c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for c in [2, -3]:  # 变换因子c\n",
    "    f_x_array_new = f_x_array + c  # 计算垂直平移后的函数值\n",
    "    plot_curve(x_array, f_x_array, x_array, f_x_array_new)  # 绘制原始和变换后的曲线"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cad8d4dc-8d03-4301-928b-22579dd3612c",
   "metadata": {},
   "source": [
    "## 水平平移"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "18f705f1-9090-4942-ac75-dcddcfd2934a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for c in [3, -1]:  # 变换因子c\n",
    "    f_x_new = 2 * exp(-((x + c) - 1)**2)  # 水平平移后的函数\n",
    "    f_x_new_fcn = lambdify([x], f_x_new)  # 将变换后的f(x)转换为可计算形式\n",
    "    f_x_array_new = f_x_new_fcn(x_array)  # 计算水平平移后的函数值\n",
    "    plot_curve(x_array, f_x_array, x_array, f_x_array_new)  # 绘制原始和变换后的曲线"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5bd15f23-8c70-4d1f-988b-6da3ea6cb1e9",
   "metadata": {},
   "source": [
    "## 垂直缩放"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ea2b7074-3843-411b-9b33-1b74b744740d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for c in [1/2, 2]:  # 变换因子c\n",
    "    f_x_array_new = c * f_x_array  # 计算垂直缩放后的函数值\n",
    "    plot_curve(x_array, f_x_array, x_array, f_x_array_new)  # 绘制原始和变换后的曲线"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "173b432b-6da9-4c26-9de1-461ee40ed328",
   "metadata": {},
   "source": [
    "## 水平缩放"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1d9f1ab5-364a-4a4c-9904-e6a10b9ea92f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for c in [1/2, 2]:  # 变换因子c\n",
    "    f_x_new = 2 * exp(-(c * x - 1)**2)  # 水平缩放后的函数\n",
    "    f_x_new_fcn = lambdify([x], f_x_new)  # 将变换后的f(x)转换为可计算形式\n",
    "    f_x_array_new = f_x_new_fcn(x_array)  # 计算水平缩放后的函数值\n",
    "    plot_curve(x_array, f_x_array, x_array, f_x_array_new)  # 绘制原始和变换后的曲线"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd8d2789-f14d-43c0-a4ed-67df4b11be6b",
   "metadata": {},
   "source": [
    "## 关于x轴对称"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "69d3e2d2-e593-4eda-aa6d-0f4457accc29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f_x_array_new = -f_x_array  # 计算关于x轴对称变换后的函数值\n",
    "plot_curve(x_array, f_x_array, x_array, f_x_array_new)  # 绘制原始和变换后的曲线"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7152e7cf-a1a2-414a-a090-08fa756504bf",
   "metadata": {},
   "source": [
    "## 关于y轴对称"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2163085e-020d-4613-bef6-6c48d7ef3340",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f_x_new = 2 * exp(-(-x - 1)**2)  # 定义关于y轴对称变换后的函数\n",
    "f_x_new_fcn = lambdify([x], f_x_new)  # 将变换后的f(x)转换为可计算形式\n",
    "f_x_array_new = f_x_new_fcn(x_array)  # 计算关于y轴对称变换后的函数值\n",
    "plot_curve(x_array, f_x_array, x_array, f_x_array_new)  # 绘制原始和变换后的曲线"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
